Some Model Assisted Estimators Using Functional Form Calibration Approach

The Model assisted estimators are approximately design unbiased, consistent and provides robustness in the case of large sample sizes. The model assisted estimators result in reduction of the design variance if underlying model reasonably defines the regression relationship. If the model is misspecified, then model assisted estimators might result in an increase of the design variance but remain approximately design unbiased and show robustness against model-misspecification. The well-known model assisted estimators, generalized regression estimators are members of a larger class of calibration estimators. Calibration method generates calibration weights that meet the calibration constraints and have minimum distance from the sampling design weights. By using different distance measures, classical calibration approach generates different calibration estimators but with asymptotically identical properties. The constraint of distance minimization was reduced for studying the properties of calibration estimators by proposing a simple functional form approach. The approach generates calibration weights that prove helpful to control the changes in calibration weights by using different choices of auxiliary variable’s functions. This paper is an extended work on model assisted approach by using functional form of calibration weights. Some new model assisted estimators are considered to get efficient and stabilized regression weights by introducing a control matrix. The asymptotic un-biasedness of the proposed estimators is verified and the expressions for MSE are derived in three different cases. A simulation study is done to compare and evaluate the efficiency of the proposed estimators with some existing model assisted estimators.

E-optimal Experimental Designs for Poisson Regression Models in Two and Three Variables

In the context of generalized linear models, most of the recent studies were on logistic regression models and many of them focussed on optimal experimental designs with concentration on D-optimality. In this research, two- and three-variable Poisson regression models were considered for E-optimization on restricted design space [0, 1]. The two-variable Poisson regression model was not optimal at 3-design points, but was found to be E-optimal at 4-design points (1, 1), (0, 0), (0, 1) and (1, 0) with equal design weights of 0.25. The three-variable Poisson regression model was E-optimal at 4-design points (0, 0, 1), (0, 1, 0), (1, 1, 1) and (1, 0, 0) with each design point having design weights of 0.25. The prediction error variance (PEV) for the two-variable Poisson regression model is 0.35 and that of the three-variable Poisson regression model is 0.68. From this research, the two-variable Poisson regression model is preferred to the three-variable Poisson regression model because of smaller PEV. Keywords: E-optimality; Fisher Information Matrix; Poisson Regression Model; Prediction Error Variance

Tuning design weights to deal with non-response in successive sampling

The estimation of finite population mean at current occasion in two occasion successive sampling in presence of non-response is investigated using tuned jackknife estimators. Based on the availability of auxiliary information at population level (Info U) and sample level (Info s) and using tuned jackknife technique, estimators have been proposed. Estimator of variance of proposed estimators have also been discussed. Different cases of occurance of non-response have been explored. The estimators are mutually compared. The properties of these estimators are studied via simulation study using natural population.

Outliers in official statistics

The purpose of this manuscript is to provide a survey on the important methods addressing outliers while producing official statistics. Outliers are often unavoidable in survey statistics. They may reduce the information of survey datasets and distort estimation on each step of the survey statistics production process. This paper defines outliers to be focused on each production step and introduces practical methods to cope with them. The statistical production process is roughly divided into the following three steps. The first step is data cleaning, and outliers to be focused are that may contain mistakes to be corrected. Robust estimators of a mean vector and covariance matrix are introduced for the purpose. The next step is imputation. Among a variety of imputation methods, regression and ratio imputation are the subjects in this paper. Outliers to be focused on in this step are not erroneous but have extreme values that may distort parameter estimation. Robust estimators that are not affected by remaining outliers are introduced. The final step is estimation and formatting. We have to be careful about outliers that have extreme values with large design weights since they have a considerable influence on the final statistics products. Weight calibration methods controlling the influence are discussed based on the robust weights obtained in the previous imputation step. A few examples of practical application are also provided briefly, although multivariate outlier detection methods introduced in this paper are mostly in the research stage in the field of official statistics.

An Appraisal of Common Reweighting Methods for Nonresponse in Household Surveys Based on the Norwegian Labour Force Survey and the Statistics on Income and Living Conditions Survey

Despite increasing efforts during data collection, nonresponse remains sizeable in many household surveys. Statistical adjustment is hence unavoidable. By reweighting the design, weights of the respondents are adjusted to compensate for nonresponse. However, there is no consensus on how this should be carried out in general. Theoretical comparisons are inconclusive in the literature, and the associated simulation studies involve hypothetical situations not all equally relevant to reality. In this article we evaluate the three most common reweighting approaches in practice, based on real data in Norway from the two largest household surveys in the European Statistical System. We demonstrate how cross- examination of various reweighting estimators can help inform the effectiveness of the available auxiliary variables and the choice of the weight adjustment method.

Adjusting for non-response in the Finnish Drinking Habits Survey

Aim: We aim to compare four different weighting methods to adjust for non-response in a survey on drinking habits and to examine whether the problem of under-coverage of survey estimates of alcohol use could be remedied by these methods in comparison to sales statistics. Method: The data from a general population survey of Finns aged 15–79 years in 2016 ( n=2285, response rate 60%) were used. Outcome measures were the annual volume of drinking and prevalence of hazardous drinking. A wide range of sociodemographic and regional variables from registers were available to model the non-response. Response propensities were modelled using logistic regression and random forest models to derive two sets of refined weights in addition to design weights and basic post-stratification weights. Results: Estimated annual consumption changed from 2.43 litres of 100% alcohol using design weights to 2.36–2.44 when using the other three weights and the estimated prevalence of hazardous drinkers changed from 11.4% to 11.4–11.8%, correspondingly. The use of weights derived by the random forest method generally provided smaller estimates than use of the logistic regression-based weights. Conclusions: The use of complex non-response weights derived from the logistic regression model or random forest are not likely to provide much added value over more simple weights in surveys on alcohol use. Surveys may not catch heavy drinkers and therefore are prone for under-reporting of alcohol use at the population level. Also, factors other than sociodemographic characteristics are likely to influence participation decisions.